🧮 algebra

1. Given the quadratic equation $$x^2 + p x + 4 = 0$$ with roots $$\alpha$$ and $$\beta$$. 2. We know from Vieta's formulas:

1. The problem is to evaluate the expression $8 - 11 \times (-6)$.\n2. According to the order of operations, multiplication is done before subtraction.\n3. Multiply $11$ by $-6$: $

1. The problem is to evaluate the expression $8 - 11 \times (-66)$. 2. According to the order of operations, multiplication comes before subtraction. So first, calculate $11 \times

1. The expression given is $8 - 11 x - 6$. 2. Usually, multiplication is implied between a number and a variable, so $11 x$ means $11\times x$.

1. The problem is to simplify the expression $8 - 11 \times -66$. 2. According to the order of operations (PEMDAS/BODMAS), we first perform the multiplication:

1. The problem is to simplify the expression $8 - 11 \times 6$. 2. According to the order of operations, multiplication is performed before subtraction.

1. The problem is to find the equation of the parabola given by $$y = x^2 + 3x + 6$$ after a rotation of 270° about the point $$(-2,4)$$. 2. First, translate the coordinate system

1. Stating the problem: Simplify the expression $$\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x}\sqrt[n]{x}$$. 2. Recall the property of radicals: $$\sqrt[n]{a}\cdot\sqrt[n]{b} = \sqrt[n]{ab}$$

1. The problem is to simplify the expression $\sqrt{x}5 - 2\sqrt{x}6$. 2. We rewrite the expression to clarify it: $5\sqrt{x} - 2\sqrt{x}6$.

1. Stating the problem: We need to evaluate the expression $\frac{\sqrt{36}}{4}$.\n2. Calculate the square root: $\sqrt{36} = 6$.\n3. Substitute back: The expression becomes $\frac

1. Problem: 30 is 20% of what number? We need to find the number $x$ such that $20\%$ of $x$ is 30.

1. The problem is to simplify the expression $\frac{\sqrt{3}}{4}$.\n2. Here, $\sqrt{3}$ is the square root of 3, and it remains as is.\n3. The denominator is 4, so the fraction can

1. The problem is to simplify or factor the expression $4x^2 - 2x^3 - 6x$. 2. First, identify the greatest common factor (GCF) of all terms. The terms are $4x^2$, $-2x^3$, and $-6x

1. The problem asks us to place the given numbers from the box onto the number line at the positions marked with a "+". 2. First, let's convert all boxed numbers to decimal form to

1. First, understand the function's formula. For example, if you have $f(x) = x^2 - 4x + 3$, this tells you how to calculate the output $y$ for each input $x$. 2. Identify key feat

**Problème 3 : Résoudre dans \(\mathbb{R}\) les équations et inéquations suivantes :** 1. \(\sqrt{x^2 - 2} = x\)

1. Find the domain and range of each relation using interval notation, and determine if it is a function. - Top-left graph (rational function with vertical asymptote at $x=1$ and h

1. Factorise each expression step-by-step. **a) $64a^2b^3 - 16b^2a^3$**

1. The problem is to simplify the expression $x^2 - 2\sqrt{x} - 4\sqrt{x}$.\n\n2. Notice that $-2\sqrt{x} - 4\sqrt{x}$ can be combined because they have like terms involving $\sqrt

1. Stating the problem: We need to graph the system of equations: $$x+2y=6$$

1. The problem is to graph the equations provided by the user. 2. However, no specific equations were given to graph.